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On partial sums of four parametric Wright function

Muhey U. Din
대한수학회 (The Korean Mathematical Society)|2022.07|대한수학회논문집 (Communications of the KMS)|제37권 제3호|pp. 681-692|DOI 10.4134/CKMS.c200469

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참고문헌

키워드

analytic functionsPartial sumsnormalized four parametric Wright function
주제분류수학

초록

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al.~\cite{din}. Some examples are also discussed for the sake of better understanding of this article.

Abstract

Special functions and Geometric function theory are close related to each other due to the surprise use of hypergeometric function in the solution of the Bieberbach conjecture. The purpose of this paper is to provide a set of sufficient conditions under which the normalized four parametric Wright function has lower bounds for the ratios to its partial sums and as well as for their derivatives. The sufficient conditions are also obtained by using Alexander transform. The results of this paper are generalized and also improved the work of M. Din et al.~\cite{din}. Some examples are also discussed for the sake of better understanding of this article.

참고문헌 (40)

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